Hydrogenation via a low energy mechanochemical approach: the MgB$_2$ case

This work aims at investigating the effect that the energy transferred during powder-to-wall collisions in a milling process without grinding media entails on solid-gas reactions. For this purpose, the synthesis of Mg(BH$_4$)$_2$ from MgB$_2$ in a pressurized hydrogen atmosphere was chosen as a model reaction. MgB$_2$ was milled under a broad set of milling parameters (i.e. milling times and rotation regimes) and the obtained product thoroughly characterized. By proving the partial formation of Mg(BH$_4$)$_2$, the results of this investigation indicate that the energy transferred to the powder bed by the powder particles colliding with the chamber wall during milling is not negligible, in particular when the milling process is protracted for a long period.


Introduction
Mechanochemistry is the branch of chemistry that studies processes that occur under mechanical energy input. Since the 1860s, the development of mechanochemical techniques increasingly influenced several technological fields among which is powder processing. These techniques found application not only in the production of fine and homogeneous powder mixtures, but also for the synthesis of advanced materials. 1 Mechanochemical processes are usually carried out via the use of high-energy mills e.g. planetary mills, roto-vibrational mills, vibration mills, attritor mills, pin mills, and rolling mills.
The milling process takes place into a specifically designed milling chamber. Several different variables influence the milling outcome, e.g. type of the mill, material of the grinding media, ballto-powder ratio (BTP), filling extent of the milling chamber, milling atmosphere, milling speed, milling time, etc... 2 Upon milling, in milling devices such as planetary mills, mechanical stresses are applied on a fraction of powder particles trapped between grinding media colliding with the wall of the milling chamber. When the mechanically applied stresses overcome the material yield point of the trapped material, complex sequences of local atomic rearrangement and subsequent equilibration stages lead to phenomena of cold work, fracture, and plastic deformation of the material particles.
This whole sequence of events can be regarded as a modification of the atomic coordination shells, which locally generates a transient energy excess in the crystal lattice. The region of the solid where the energy excess is located moves away from equilibrium conditions generating a so-called local excited state (LES). 3 The formation of LESs is considered to be the reason for the unusual chemical behavior observed in processes taking place under mechanochemical input (e.g. enhanced absorption of gaseous phases). In a milling process, the energy transferred as the consequence of collisions between powder particles and chamber wall is not considered. This is mostly due to the expected low relevance that the energy transferred through these collisions has on the overall mechanochemical process when compared to the energy transferred during the impacts of the grinding media with the chamber walls.
However, at high temperatures (i.e. above 500 °C) the final solid decomposition product of Mg(BH4)2 is MgB2.It must be noticed that during the decomposition process the possibility of releasing small quantities of B2H6 was also reported. 5,32,35,37 In literature four different crystalline magnesium borohydride polymorphs are reported, i.e. hexagonal α (P6122), 33,38-40 orthorhombic β (Fddd), 35,41 cubic γ (Id-3a) 42 and trigonal ζ (P-3m1) 43 . Depending on the utilized synthesis method, it is possible to obtain magnesium borohydride also in an amorphous state. 44 The synthesis of Mg(BH4)2 via wet chemistry methods is challenging since several possible solvent adducts can be formed (e.g. diethyl ether, toluene/heptane, and amine solutions). 38 Solvent-free processes to synthesize magnesium borohydride based on the metathesis reaction of MgCl2 with NaBH4 and LiBH4 performed under mechanochemical input were also reported. 32 The possibility to convert MgB2 into β-Mg(BH4)2 with a conversion yield of 75% was reported to be possible at 400 °C and under a hydrogen pressure of 950 bar. 37

Experimental
The MgB2 used in this work was purchased from Alfa Aesar in powder form with a purity equal to 95%. The material were mixed (no grinding media were used) under a reactive atmosphere of hydrogen by using a stainless steel pressure chamber from Evico Magnetics mounted on a Fritsch Planetary Mono Mill PULVERISETTE 6. Two MgB2 batches of 15 g were used. The first batch was the as-received MgB2: this material was divided into three parts (5 grams for each test), which were then mixed for 10, 25, and 50 hours at 550 rpm, respectively, under 100 bar of hydrogen. The second batch was prepared starting from the pre-milled MgB2 (10 hours at 550 rpm using a BTP ratio of 10:1) divided into three parts (5 grams for each test) and then mixed for  Figure 6) was acquired at room temperature at a spinning speed of 10 kHz, using a ramp cross-polarization pulse sequence with a 90° 1 H pulse of 3.80 μs, a contact time of 1 ms, an optimized recycle delay of 3.2 s and a number of scans of 32750. A twopulse phase modulation (TPPM) decoupling scheme was used, with a radiofrequency field of 69.4 kHz. The 11 B chemical shift scale was calibrated through the 11 B signal of external standard NaBH4 (at -42.0 ppm with respect to BF3·O(CH2CH3)2). The spinning sidebands are indicated by the asterisk symbol "*".
The first-principles calculation of NMR parameters was carried out with the gauge-including projector augmented-wave (GIPAW) 46 and the projector augmented-wave (PAW) method as implemented in the Vienna ab initio simulation package (VASP) 47 . Exchange and correlation effects were described using the generalized gradient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE) functional. 48 The plane wave expansion includes all plane waves within a kinetic energy cut-off of 600 eV. The sampling of the Brillouin zone was performed using a Monkhorst-Pack scheme with a dense k-mesh corresponding to a k-spacing of 0.2 Å. The structures were optimized prior to GIPAW calculations until the forces on each atom were less than 0.01 eV/Å.
GIPAW calculations yielded the principal components of the absolute shielding tensor (σ). The isotropic chemical shift (δiso) could then be determined by comparing a model system computed at the same level to the known experimental shift (δiso e ) to obtain the reference isotropic shielding (δiso r ). In this study, δiso r is set as -101.39 ppm to fit the δiso e of Mg(BH4)2 and MgB2.

Results
The starting materials, and the same after mixing in hydrogen atmosphere, were characterized by means of ex-situ PXD. The acquired diffraction patterns are displayed in Figure 1. shown on the right-hand side (B). All the specimens appear to be composed mostly of crystalline MgB2 plus a small amount of magnesium. Despite the apparently identical composition, for the MgB2 phase it is possible to perceive a progressive increment of the value of full width at half maximum (FWHM) of the material treated under a hydrogen atmosphere. This effect is more marked for the material that underwent ball milling prior to the hydrogen treatment ( Fig 1B).
Considering that the diffraction measurements were acquired all at the same temperature (room temperature) and using the same instrumental setup, the broadness of diffraction peaks can be related only to the size of the MgB2 crystallites and to its lattice strains. In order to quantify variations of the crystallite size and lattice strain, the Rietveld refinement of all the diffraction patterns was carried out. The refinement results are summarized in Table 1.  To study the morphological features of the starting materials and the changes which they supposedly underwent during mixing, all the investigated specimens were characterized by the SEM technique, and the results are summarized in Figure 2.
The    that some B2O3 might be present in the analyzed samples was considered; however, after a careful analysis of the spectra we established the quantity of this phase to be neglectable. From the integration of the area enclosed in the center and spinning sidebands of the spectra of Figure 5B we estimated the following boron distribution (Table 2):

Discussion
The results reported in the previous section indicate that the energy transferred during powderto-wall collisions in a milling process cannot be neglected. In fact, for the chosen model reaction, the transferred energy not only allowed to refine the material microstructure (Figure 1 and 2) but it also allowed its partial hydrogenation (Figure 3 trigger the reaction. 53,54,55 However, the formation of MgBH4 here described and performed without any grinding media, was quite unexpected. As emerged from the SEM analyses reported in Figure   2 and the volumetric analyses of Figure 3, the particle reactivity seems to be connected to their dimension. For the hydrogenation processes performed under identical rotation regime, extent of time, and consequently milling chamber temperature (lower than 60 °C), the reduced MgB2 particle dimensions allowed achieving a larger degree of conversion of MgB2 into Mg(BH4)2 i.e.
2.1 wt% for 550 rpm and 0.26 wt% for 50 h. Interestingly, for the material milled for the same extent of time (e.g. 350 rpm, 450 rpm, and 550 rpm) a clear correlation between the increased number of rpm and the yield of the conversion is seen (Table 2). Therefore, not only a mechanical input appears to be necessary to initiate the hydrogenation reaction, but also the magnitude of the energy transferred during the collisions appears to play an important role in the conversion of MgB2 into Mg(BH4)2. To further investigate this aspect, it is plausible to estimate the collision energy for each particle, assuming that their motion during rotation can be approximately treated as the balls in a mechanochemical reactor. For this purpose, it is then possible to exploit the model proposed by Burgio et al. 56 According to this work, the total energy (ΔE*), released by one particle in a mechanochemical reactor, can be calculated by the equation (5): where ϕ is the degree of milling which can be approximated to 1 due to the small diameter of particles, mb the mass of each particle, i.e. 2.32 * 10 -9 kg considering a starting particle dimension of 120 μm, a density of 2.57 g/cm 3 , and a spherical geometry of the particles, Ωp the rotation velocity of the plate (rad/s), ωv the rotation velocity of chamber (rad/s), rv the chamber radius (m), Rp the plate radius (m) and dp the particle diameter (1.2 *10 -4 m) . The resulting total energy which each particle dissipated impacting the wall of the chamber is reported in Table 3: Table 3: Total energy which each particle of 350 rpm, 450 rpm, and 550 rpm dissipates impacting the wall of the chamber.  appeared also in the direct 11 B measurements of Figure 5 and is due to the formation of Mg(BH4)2.

Sample name
Thus, the signal visible in the direct 11 B spectra at 3.5 ppm ( Figure 5) corresponds to 11 Figure S2 and Table S1, respectively in the Supplementary Information. Mg-B compounds can be ruled out seeing as their computed δiso values lie out of the range of the signal in question, which is localized around 3 ppm. As Table 4 shows, structures containing B12 clusters as building units give chemical shifts in the expected range, which is in agreement with work by others. 58,59 The structures of both α-and β-rhombohedral boron phases are closely related and contain B12 subunits. Since both allotropes could potentially form under the experimental conditions, they are both likely candidates for the origin of the unidentified signal in the spectrum, although the disordered β-phase is marginally more stable. 60 The lack of diffraction peaks associated to the presence of this boron phase in the PXD analyses of Figure 1 might be justified by the existence of this phase in a nanostructured state.

Conclusion
In this work, the effect of the energy transferred through powder-to-wall collisions during the milling process of MgB2 under a hydrogen atmosphere was studied. The obtained pieces of evidence demonstrated that this energy allowed the partial hydrogenation of the starting MgB2 to form Mg(BH4)2. Owing to a series of MAS NMR measurements and numerical simulations it has been possible to find out that consequently to the mechanochemical treatment a fraction of the starting MgB2 is converted in α-or β-rhombohedral boron and Mg/MgH2. Taking advantage of the kinematic model developed by Burgio and co-workers, an attempt to estimate the collision energy for each particle was made for the first time, to the best of the authors' knowledge. The results of this calculation revealed that for the applied measurement conditions and powder features, the energy transferred during a single powder-to-wall impact is 5-6 order of magnitude smaller than the typical energy transferred during ball-to-wall impact during a similar milling process carried out in the presence of grinding media. This work opens a new frontier on the study of the synthesis of material under low-energy mechanochemical input in reactive atmospheres.